Definition 6 (Tightness of Decompositions)  [1]}
A decomposition function \(f^1_d\)  for system (REF ) is tighter than decomposition function \(f^2_d\) , if  for all \(z \le \hat{z}\) ,
\( f^2_d(z,\hat{z}) \le f^1_d(z,\hat{z}) \ \text{and} \ f^1_d(\hat{z},{z}) \le f^2_d(\hat{z},{z}).\) 
